This is an announcement for the paper "Sharp quantitative isoperimetric inequalities in the $L^1$ Minkowski plane" by Benoit Kloeckner. Abstract: We prove that a plane domain which is almost isoperimetric (with respect to the $L^1$ metric) is close to a square whose sides are parallel to the coordinates axis. Closeness is measured either by $L^\infty$ Haussdorf distance or Fraenkel asymmetry. In the first case, we determine the extremal domains. Archive classification: math.FA math.DG Mathematics Subject Classification: MSC 51M16, 51M25, 49Q20 Remarks: 9 pages The source file(s), central_square.pstex: 6034 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0907.4945 or http://arXiv.org/abs/0907.4945 or by email in unzipped form by transmitting an empty message with subject line uget 0907.4945 or in gzipped form by using subject line get 0907.4945 to: math@arXiv.org.